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Lesson 6.4

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Name
Class
Date
Practice
6-4
Form K
Properties of Rhombuses, Rectangles, and Squares
Decide whether the parallelogram is a rhombus, a rectangle, or
a square. Explain.
1.
2.
rhombus; four congruent
sides, no right angles
rectangle; opposite sides
congruent, four right angles
3.
4.
square; four right angles
and four congruent sides
rectangle; right angles,
opposite sides congruent
Find the measures of the numbered angles in each rhombus.
5.
To start, a diagonal of a rhombus forms
an isosceles triangle with congruent
base angles.
1
2
3
38
u 5 38.
So, m/ 1
38; 104; 104
6.
2
7.
1
4
73
2
20; 90; 70; 20
9.
106
106; 37; 37
53.5; 53.5; 53.5; 53.5
1
4
3
2
3
8.
1
3
To start, the diagonals of a rhombus
are perpendicular.
70
So, m/ 2
u 5 90.
10.
4
1
3
2
1
4
52
2
3
25
38; 90; 38; 52
90; 65; 65; 25
Prentice Hall Foundations Geometry • Teaching Resources
Copyright В© by Pearson Education, Inc., or its affiliates. All Rights Reserved.
35
Name
6-4
Class
Date
Practice (continued)
Form K
Properties of Rhombuses, Rectangles, and Squares
Algebra QRST is a rectangle. Find the value of x and the length of
each diagonal.
11. QS 5 x and RT 5 6x 2 10 2; 2
To start, write an equation to show the
diagonals are congruent.
9 5 9 x; 6x 2 10
12. QS 5 4x 2 7 and RT 5 2x 1 11
9; 29
13. QS 5 5x 1 12 and RT 5 6x 2 2
14; 82
14. QS 5 6x 2 3 and RT 5 4x 1 19
11; 63
15. QS 5 x 1 45 and RT 5 4x 2 45
30; 75
Determine the most precise name for each quadrilateral.
16.
square
6
17.
rhombus
6
6
6
18.
19.
rectangle
3
3
3
3
rhombus
Determine whether each statement is true or false. If it is false, rewrite the
sentence to make it true. If it is true, list any other quadrilaterals for which
the sentence would be true.
20. Rhombuses have four congruent sides. true; squares
21. Rectangles have four congruent angles. true; squares
22. The diagonals of a rectangle bisect the opposite angles. False; the diagonals of
a rhombus bisect the opposite angles.
23. The diagonals of a rhombus are always congruent. False; the diagonals of rectangles
or squares are congruent, but not all rhombuses are rectangles or squares.
Algebra Find the values of the variables. Then find the side lengths.
24.
2y 4
x 14
4x 22
25.
4; 7; 18
5y 15
3y 3
5x 2
13; 9; 30
3y 3
2x 4
Square
Rhombus
Prentice Hall Foundations Geometry • Teaching Resources
Copyright В© by Pearson Education, Inc., or its affiliates. All Rights Reserved.
36
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